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Constructive bounds on ordered factorizations. (English) Zbl 1090.05004

Summary: The number of ways to factor a natural number \(n\) into an ordered product of integers, each factor greater than one, is called the ordered factorization of \(n\) and is denoted \(H(n)\). We show upper and lower bounds on \(H(n)\) with explicit constructions.

MSC:

11N56 Rate of growth of arithmetic functions
05A17 Combinatorial aspects of partitions of integers
05A15 Exact enumeration problems, generating functions
05A05 Permutations, words, matrices
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